Codes to solve System Dynamics homework 1, WITHOUT WARRANTY.

SDHW1.m

syms A;
syms t positive;
syms t_0 positive;
syms s;
syms omega positive;

sig1 = A * heaviside(t) - A * heaviside(t - t_0);
sig2 = (heaviside(t) - heaviside(t - 2*pi/omega))*sin(omega * t)*A;

sig1 = laplace(sig1, t, s);
sig2 = simplify(expand(laplace(sig2, t, s)));

%(a)
sys = 1/(s^2 + 5*s + 6);
res(1) = ilaplace(sys * sig1);
res(2) = ilaplace(sys * sig2);

%(b)
sys = 1/(s^2 + 2*s + 2);
res(3) = ilaplace(sys * sig1);
res(4) = ilaplace(sys * sig2);

%(c)
figure(1);
for i = [1 3]
    p = res(i);
    p = matlabFunction(p(1));
    tau = 0:0.001:15;
    subplot(2, 2, i);hold on;
    axis([0 15 -0.6 0.6]);
    for j = 1:5
        lab = strcat('t_0 = ', num2str(j));
        plot(tau, p(1, tau, j), 'DisplayName', lab);
        set(gcf,'PaperUnits','inches','PaperPosition',[0 0 4 3]);
    end
    legend('show');
end

for i = [2 4]
    p = res(i);
    p = matlabFunction(p(1));
    tau = 0:0.001:15;
    subplot(2, 2, i);hold all;
    axis([0 15 -0.6 0.6]);
    for j = 1:5
        lab = strcat('\omega = ', num2str(j));
        plot(tau, p(1, tau, j), 'DisplayName', lab);
        set(gcf,'PaperUnits','inches','PaperPosition',[0 0 40 30]);
    end
    legend('show');
end

print('-dpng','-r0','SD HW1.png')